Vanishing singularity in hard impacting systems

Discrete and Continuous Dynamical Systems - Series B

Volumn 16, Issue 1, 2011, Pages 319-332

  Kundu, Soumya ^a   Banerjee, Soumitro ^b   Giaouris, Damian ^c  

^a UNIVERSITY OF MICHIGAN   (United States)

^b INDIAN INSTITUTE OF SCIENCE EDUCATION AND RESEARCH KOLKATA   (India)

^c NEWCASTLE UNIVERSITY   (United Kingdom)

Author keywords

Border collision bifurcation; Grazing; Impact oscillator; Nonsmooth system

Indexed keywords

EID: 79959238741     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2011.16.319     Document Type: Article

References (17)

1. S. W. Shaw and P. J. Holmes, A periodically forced piecewise linear oscillator, Journal of Sound & Vibration, 90(1983), 129-155. (Pubitemid 14455664)
2. F. Peterka and J. Vacik, Transition to chaotic motion in mechanical systems with impacts, Journal of Sound and Vibration, 154(1992), 95-115.
3. B. Blazejczyk-Okolewska and T. Kapitaniak, Co-existing attractors of impact oscillator, Chaos, Solitons & Fractals, 9(1998), 1439-1443. (Pubitemid 128435206)
4. S. Lenci and G. Rega, A procedure for reducing the chaotic response region in an impact mechanical system, Nonlinear Dynamics, 15(1998), 391-409. (Pubitemid 128513971)
5. D. J. Wagg, G. Karpodinis and S. R. Bishop, An experimental study of the impulse response of a vibro-impacting cantilever beam, Journal of Sound & Vibration, 228(1999), 243-264. (Pubitemid 129531616)
6. E. K. Ervin and J. A. Wickert, Experiments on a beam-rigid body structure repetitively impacting a rod, Nonlinear Dynamics, 50(2007), 701-716. (Pubitemid 47536435)
7. J. Ing, E. Pavlovskaia and M. Wiercigroch, An experimental study into the bilinear oscillator close to grazing, In "International Symposium on Nonlinear Dynamics, Journal of Physics: Conference Series", 96(2007), 012119.
8. A. B. Nordmark, Non-periodic motion caused by grazing incidence in an impact oscillator, Journal of Sound and Vibration, 145(1991), 279-297.
9. A. B. Nordmark, Universal limit mapping in grazing bifurcations, Phys. Rev. E, 55(1997), 266-270. (Pubitemid 127607436)
10. M. di Bernardo, C. J. Budd, A. R. Champneys and P. Kowalczyk, "Piecewise-smooth Dynamical Systems: Theory and Applications", Springer Verlag (Applied Mathematical Sciences), London, 2008.
11. Y. Ma, M. Agarwal and S. Banerjee, Border collision bifurcations in a soft impact system, Physics Letters A, 354(2006), 281-287. (Pubitemid 43668650)
12. Y. Ma, J. Ing, S. Banerjee, M. Wiercigroch and E. Pavlovskaia, The nature of the normal form map for soft impacting systems, International Journal of Nonlinear Mechanics, 43(2008), 504-513.
13. J. Ing, E. Pavlovskaia, M. Wiercigroch and S. Banerjee, Experimental study of impact oscillator with one-sided elastic constraint, Philosophical Transactions of the Royal Society of London, Part A, 366(2008), 679-704.
14. R. I. Leine and H. Nijmeijer, "Dynamics and Bifurcations in Non-Smooth Mechanical Systems", Springer Verlag, Berlin, 2004.
15. S. Banerjee and C. Grebogi, Border collision bifurcations in two-dimensional piecewise smooth maps, Physical Review E, 59(1999), 4052-4061. (Pubitemid 129690216)
16. S. Banerjee, P. Ranjan and C. Grebogi, Bifurcations in two-dimensional piecewise smooth maps - theory and applications in switching circuits, IEEE Transactions on Circuits and Systems-I, 47(2000), 633-643.
17. H. Dankowicz and F. Svahn, On the stabilizability of near-grazing dynamics in impact oscillators, Int. J. Robust & Nonlinear Control, 17(2007), 1405-1429. (Pubitemid 47509835)